9/23/2023

 Today I submitted my application for my local ARML team selection, which required solving two problems. I'm not allowed to talk about them here, though.

I'm currently working on this cool olympiad problem: 

Problem

Numbers $1,2,...,2n$ are partitioned into two sequences $a_1<a_2<...<a_n$ and $b_1>b_2>...>b_n$. Prove that number

$$W=|a_1-b_1|+|a_2-b_2|+...+|a_n-b_n|$$

is a perfect square.

This problem is stumping me! I'll post a solution later if I find one.